The dimensional formula for specific heat is

Options

A. `M^(0)L^(2)T^(-2)`
B. `M^(1)L^(2)T^(-2)K^(-1)`
C. `M^(0)L^(2)T^(-2)K^(-1)`
D. `M^(1)L^(2)T^(-2)`

Answer

To find the dimensional formula for specific heat, we start with the definition of specific heat and analyze the components involved.

### Step-by-Step Solution:

1. **Understanding Specific Heat**:
Specific heat (s) is defined as the amount of heat (q) required to raise the temperature of a unit mass (m) of a substance by one degree Celsius (or one Kelvin). The formula can be expressed as:
\[ s = \frac{q}{m \Delta T} \]
where \( \Delta T \) is the change in temperature.

2. **Identifying Dimensions**:
- **Heat (q)**: The dimension of heat is the same as that of energy. Energy can be expressed as work done, which is force multiplied by displacement.
- **Force**: The dimension of force is given by:
\[ [F] = [M][L][T^{-2}] \]
- **Displacement**: The dimension of displacement is:
\[ [L] \]
- Therefore, the dimension of energy (or heat) is:
\[ [q] = [F][L] = [M][L][T^{-2}][L] = [M][L^{2}][T^{-2}] \]

3. **Mass (m)**:
The dimension of mass is:
\[ [m] = [M] \]

4. **Change in Temperature (\( \Delta T \))**:
The dimension of temperature change is:
\[ [\Delta T] = [K] \]
where \( K \) represents Kelvin.

5. **Combining Dimensions**:
Now, substituting the dimensions into the specific heat formula:
\[ [s] = \frac{[q]}{[m][\Delta T]} = \frac{[M][L^{2}][T^{-2}]}{[M][K]} \]

6. **Simplifying**:
When we simplify this expression, the mass \( [M] \) cancels out:
\[ [s] = \frac{[L^{2}][T^{-2}]}{[K]} = [L^{2}][T^{-2}][K^{-1}] \]

### Final Answer:
Thus, the dimensional formula for specific heat is:
\[ [L^{2}][T^{-2}][K^{-1}] \]